Numbers and Operations

Chapter 1

Numbers and Operations

Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Functions

1. Determines whether a relation is a function

A relation is any pairing of inputs (x-values) with outputs (y-values). A function is a relation where each input corresponds to exactly one output. This uniqueness requirement is the defining property of a function.

Ways to determine if a relation is a function

1. From ordered pairs or a table of values

Check whether any input x is repeated with different outputs y. If so, the relation is not a function.

• Example: {(1, 2), (2, 4), (3, 6)} is a function, since each x-value is unique.
• Example: {(1, 2), (1, 3), (2, 5)} is not a function, because input x = 1 maps to two different outputs (2 and 3).

In tables, the same logic applies. If one row has x = 5 and y = 10, and another row has x = 5 and y = 12, the relation is not a function.